Solve by completing the square: $$(x + 8)^2 - 5 = 0$$

$$x = -8 \\ x = -8 \\pm \\sqrt{5}$$

What does it mean to complete the square?

Completing the square is a method used to solve quadratic equations by rewriting them in the form $$(x - p)^2 = q$$ .

What is the discriminant in a quadratic equation?

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots of the equation.

What are imaginary numbers?

Imaginary numbers are numbers that can be written as $$bi$$ where $$b$$ is a real number and $$i$$ is the imaginary unit, defined as $$i = \sqrt{-1}$$ .

What is the vertex form of a quadratic function?

The vertex form is $$y = a(x - h)^2 + k$$ where (h, k) is the vertex of the parabola.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line that divides the parabola into two mirror images, given by $$x = -\frac{b}{2a}$$ .

What is the significance of the roots of a quadratic equation?

The roots of a quadratic equation are the x-values where the graph intersects the x-axis, indicating the solutions to the equation.

How do you factor a quadratic equation?

To factor a quadratic equation, find two numbers that multiply to $$c$$ and add to $$b$$ , then express it as $$(x - p)(x - q) = 0$$ .

What is the standard form of a quadratic function?

The standard form is $$f(x) = ax^2 + bx + c$$ where a, b, and c are constants.

Module 3 Final Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

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x = 4 and x = 5

2.

FLASHCARD QUESTION

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8

3.

FLASHCARD QUESTION

Front

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4.

FLASHCARD QUESTION

Front

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5.

FLASHCARD QUESTION

Front

Back

x = -6 and x = -1

6.

FLASHCARD QUESTION

Front

Definition of a quadratic equation

Back

7.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

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